Special Cases and Patterns
Part of Quadratic Expressions · GCSE GCSE Mathematics revision
This deep dive covers Special Cases and Patterns within Quadratic Expressions for GCSE Mathematics. Revise Quadratic Expressions in Algebra for GCSE Mathematics with 12 exam-style questions and 22 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 6 of 8 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 6 of 8
Practice
12 questions
Recall
22 flashcards
Special Cases and Patterns
Perfect Square Trinomials
These follow the pattern: x² + 2ax + a² = (x + a)²
Recognition tip: The constant term is the square of half the coefficient of x
Example: x² + 12x + 36
Half of 12 = 6, and 6² = 36 ✓
Therefore: x² + 12x + 36 = (x + 6)²
Difference of Two Squares
Pattern: x² - a² = (x + a)(x - a)
Recognition tip: Two square terms subtracted
Example: x² - 25 = x² - 5² = (x + 5)(x - 5)
When Factorising Isn't Possible
Not all quadratics can be factorised using integers
Example: x² + x + 1
Need two numbers that add to 1 and multiply to 1
No integer solutions exist - this quadratic is "irreducible" over integers
Keep building this topic
Read this section alongside the surrounding pages in Quadratic Expressions. That gives you the full topic sequence instead of a single isolated revision point.
Practice Questions for Quadratic Expressions
Expand (x + 5)².
Explain how to recognise whether x² + 12x + 36 is a perfect square trinomial, and write it in factorised form.
Quick Recall Flashcards
12 questions on Quadratic Expressions — practise free
Instant marking, adaptive difficulty, and 22 spaced repetition flashcards. Free until your GCSEs.
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